I thought he'd been retconned to being this way from the start?
Its established that the Waynes and the Kanes didn't get along. In fact, the New 52 really emphasized this aspect - there was a zero issue back in 2012 in which the Kane family tries to steal the Wayne fortune since Bruce was technically missing, presumed dead (during his years abroad) and Alfred was the only one standing in the way. Thomas Wayne literally trusted his butler to protect his son's inheritance from his wife's family!
I admit I haven't read it (no interest in the N52 setup in regards to how long he's been Batman, ages of boys when becoming Robin, etc.). The problem pre-dates N52, though. Ever since living relatives were introduced in post-COIE. Then that brings up another problem I have - good characters turned bad. People who used to be nice folks are now evil (or at least jerkish like Hal's brother). Like Uncle Philip. Pop Haly. Zor-El, Jor-El, Allura. Wally's dad. Duela Dent. Sardath. Jean Loring. Jericho. And so forth and so on. Some in reboots, some just in storylines. Some of which had bad continuity or made no sense. I don't like good characters being remade as bad. Just a thing with me. Particularly irritating when it's done with relatives, because absolutely no one is allowed to actually have good family relations - not even if their family members are dead. Not "dramatic" enough. See also: adding angsty backstory where not originally present, as with Barry.
And still doesn't deal with Jacob Kane - was he a money-stealer, too, or just inappropriate for some other reason. But even so, the entire Kane family is bad, except the one Thomas married. Yeah.
Yeah, early post-COIE Bruce has some really bad behavior. With Dick and Jason and colleagues. But the way he reacted to Dick coming back and trying to talk to him and his reasons for taking Jason in and making him Robin - they were really hitting the "emotionally stunted" notes there. Though another comic would make excuses for him (when Dick and and Roy were talking when Roy was tricking Dick so he could get Lian, I think).And while he started out healthier in Year One, they did sort of retcon more of an edge back onto him earlier in his career. See the split with Dick pre-COIE vs. after. He acts more like a mature adult before the reboot.
I don't find it less independent with Bruce because of how Alfred's treated (very different case with earlier stories with Kate and her dad, IMO). Alfred, by and large, doesn't get to make any decisions. He doesn't have any power or much influence. Which is slightly odd if he raised him, but not unbelievable. A parent's influence should wane one one is in adulthood, IMO.Plus, if Alfred hangs around as a surrogate father, it makes Bruce seem a bit less independent. He doesn't need a replacement father figure and I'm not sure if he even wants one. Alfred works better as an older peer he meets as an adult, IMO.
There's the weirdness of Alfred remaining employed as butler. As someone said in early days of watching Gotham - Alfred being both Bruce's employee and his guardian makes for a very tangled web in terms of authority/hierarchy and is unlikely to be the best setup for raising a healthy child. And years later, Alfred's still an employee (or an employee again?) instead of just being a father figure. One or the other works, but both gives it a weird dynamic that is only occasionally addressed.
I do think it largely an issue of coincidental timing rather than real intent to make Alfred an inadequate guardian. Bruce was becoming more emotionally troubled in the comics during a broadly similar timeframe as Alfred was being rewritten as a father figure, but they weren't meant to be connected. But the end result is still there.